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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 17424bt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17424.t2 | 17424bt1 | \([0, 0, 0, -363, -10406]\) | \(-121\) | \(-43717791744\) | \([]\) | \(9216\) | \(0.72449\) | \(\Gamma_0(N)\)-optimal |
17424.t1 | 17424bt2 | \([0, 0, 0, -523083, 145619386]\) | \(-24729001\) | \(-640072188923904\) | \([]\) | \(101376\) | \(1.9234\) |
Rank
sage: E.rank()
The elliptic curves in class 17424bt have rank \(0\).
Complex multiplication
The elliptic curves in class 17424bt do not have complex multiplication.Modular form 17424.2.a.bt
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.